%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV227^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:55:38 AM UTC 2026 % Result : Theorem 0.36s 0.55s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV227^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.14/0.34 % Computer : n029.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Jun 2 18:20:47 EDT 2026 % 0.14/0.34 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.36/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.55 % SZS status Theorem % 0.36/0.55 % SZS output start Proof % 0.36/0.55 ( % 0.36/0.55 (declare-sort tptp.a 0) % 0.36/0.55 (declare-const tptp.x (-> tptp.a Bool)) % 0.36/0.55 (declare-const tptp.y (-> tptp.a Bool)) % 0.36/0.55 (define @t1 () (@var "Xx0" tptp.a)) % 0.36/0.55 (define @t2 () (@var "S" (-> tptp.a Bool))) % 0.36/0.55 (define @t3 () (_ @t2 @t1)) % 0.36/0.55 (define @t4 () (or (= @t2 tptp.x) (= @t2 tptp.y))) % 0.36/0.55 (define @t5 () (and @t4 @t3)) % 0.36/0.55 (define @t6 () (@list @t2)) % 0.36/0.55 (define @t7 () (exists @t6 @t5)) % 0.36/0.55 (define @t8 () (@list @t1)) % 0.36/0.55 (define @t9 () (lambda @t8 @t7)) % 0.36/0.55 (define @t10 () (@var "Xz" tptp.a)) % 0.36/0.55 (define @t11 () (lambda (@list @t10) (or (_ tptp.x @t10) (_ tptp.y @t10)))) % 0.36/0.55 (define @t12 () (= @t11 @t9)) % 0.36/0.55 (define @t13 () (not @t12)) % 0.36/0.55 (define @t14 () (@purify @t11)) % 0.36/0.55 (define @t15 () (not (tptp.y @t1))) % 0.36/0.55 (define @t16 () (not (tptp.x @t1))) % 0.36/0.55 (define @t17 () (lambda @t8 (not (and @t16 @t15)))) % 0.36/0.55 (define @t18 () (@purify @t17)) % 0.36/0.55 (define @t19 () (= @t11 @t17)) % 0.36/0.55 (define @t20 () (not (= tptp.y tptp.y))) % 0.36/0.55 (define @t21 () (or @t20 @t15)) % 0.36/0.55 (define @t22 () (@var "BOUND_VARIABLE_7461" (-> tptp.a Bool))) % 0.36/0.55 (define @t23 () (not (_ @t22 @t1))) % 0.36/0.55 (define @t24 () (not (= tptp.y @t22))) % 0.36/0.55 (define @t25 () (@list @t22)) % 0.36/0.55 (define @t26 () (or @t24 @t24 @t23)) % 0.36/0.55 (define @t27 () (or @t24 @t23)) % 0.36/0.55 (define @t28 () (forall @t25 @t27)) % 0.36/0.55 (define @t29 () (not (= tptp.x tptp.x))) % 0.36/0.55 (define @t30 () (or @t29 @t16)) % 0.36/0.55 (define @t31 () (@var "BOUND_VARIABLE_7452" (-> tptp.a Bool))) % 0.36/0.55 (define @t32 () (not (_ @t31 @t1))) % 0.36/0.55 (define @t33 () (not (= tptp.x @t31))) % 0.36/0.55 (define @t34 () (@list @t31)) % 0.36/0.55 (define @t35 () (or @t33 @t33 @t32)) % 0.36/0.55 (define @t36 () (or @t33 @t32)) % 0.36/0.55 (define @t37 () (forall @t34 @t36)) % 0.36/0.55 (define @t38 () (_ @t2 @t1)) % 0.36/0.55 (define @t39 () (not @t38)) % 0.36/0.55 (define @t40 () (= tptp.y @t2)) % 0.36/0.55 (define @t41 () (not @t40)) % 0.36/0.55 (define @t42 () (or @t41 @t39)) % 0.36/0.55 (define @t43 () (forall @t6 @t42)) % 0.36/0.55 (define @t44 () (@list @t2)) % 0.36/0.55 (define @t45 () (= tptp.x @t2)) % 0.36/0.55 (define @t46 () (not @t45)) % 0.36/0.55 (define @t47 () (or @t46 @t39)) % 0.36/0.55 (define @t48 () (forall @t6 @t47)) % 0.36/0.55 (define @t49 () (and @t48 @t43)) % 0.36/0.55 (define @t50 () (and @t46 @t41)) % 0.36/0.55 (define @t51 () (not @t3)) % 0.36/0.55 (define @t52 () (or @t50 @t51)) % 0.36/0.55 (define @t53 () (or @t45 @t40)) % 0.36/0.55 (define @t54 () (and @t53 @t3)) % 0.36/0.55 (define @t55 () (forall @t6 (not @t54))) % 0.36/0.55 (define @t56 () (not @t55)) % 0.36/0.55 (define @t57 () (@const 0 tptp.a)) % 0.36/0.55 (define @t58 () (tptp.y @t57)) % 0.36/0.55 (define @t59 () (not @t58)) % 0.36/0.55 (define @t60 () (tptp.x @t57)) % 0.36/0.55 (define @t61 () (not @t60)) % 0.36/0.55 (define @t62 () (and @t61 @t59)) % 0.36/0.55 (define @t63 () (not @t62)) % 0.36/0.55 (define @t64 () (or @t60 @t58)) % 0.36/0.55 (define @t65 () (_ tptp.y @t57)) % 0.36/0.55 (define @t66 () (_ tptp.x @t57)) % 0.36/0.55 (define @t67 () (or @t66 @t65)) % 0.36/0.55 (define @t68 () (= (_ @t11 @t57) @t67)) % 0.36/0.55 (define @t69 () (_ @t14 @t57)) % 0.36/0.55 (define @t70 () (= (_ @t17 @t57) @t63)) % 0.36/0.55 (define @t71 () (_ @t18 @t57)) % 0.36/0.55 (define @t72 () (= @t71 @t69)) % 0.36/0.55 (define @t73 () (not @t72)) % 0.36/0.55 (define @t74 () (= @t18 @t14)) % 0.36/0.55 (define @t75 () (or @t74 @t73)) % 0.36/0.55 (define @t76 () (= @t64 @t63)) % 0.36/0.55 (define @t77 () (not @t64)) % 0.36/0.55 (define @t78 () (@list true true false)) % 0.36/0.55 (define @t79 () (@list @t76 @t62 @t64)) % 0.36/0.55 (define @t80 () (@list true true)) % 0.36/0.55 (define @t81 () (@list @t58 @t60)) % 0.36/0.55 (assume @p1 @t13) % 0.36/0.55 (assume @p2 true) % 0.36/0.55 (step @p3 :rule eq-symm :args (@t14 @t18)) % 0.36/0.55 (step @p4 :rule eq-refl :args (@t17)) % 0.36/0.55 (step @p5 :rule skolem_intro :args (@t18)) % 0.36/0.55 (step @p6 :rule refl :args (@t17)) % 0.36/0.55 (step @p7 :rule cong :premises (@p6 @p5) :args ((= @t17 @t18))) % 0.36/0.55 (step @p8 :rule trans :premises (@p7 @p4)) % 0.36/0.55 (step @p9 :rule true_elim :premises (@p8)) % 0.36/0.55 (step @p10 :rule eq-refl :args (@t11)) % 0.36/0.55 (step @p11 :rule skolem_intro :args (@t14)) % 0.36/0.55 (step @p12 :rule refl :args (@t11)) % 0.36/0.55 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t11 @t14))) % 0.36/0.55 (step @p14 :rule trans :premises (@p13 @p10)) % 0.36/0.55 (step @p15 :rule true_elim :premises (@p14)) % 0.36/0.55 (step @p16 :rule cong :premises (@p15 @p9) :args (@t19)) % 0.36/0.55 (step @p17 :rule trans :premises (@p16 @p3)) % 0.36/0.55 (step @p18 :rule cong :premises (@p17) :args ((not @t19))) % 0.36/0.55 (step @p19 :rule aci_norm :args ((= (or false @t15) @t15))) % 0.36/0.55 (step @p20 :rule refl :args (@t15)) % 0.36/0.55 (step @p21 :rule evaluate :args ((not true))) % 0.36/0.55 (step @p22 :rule eq-refl :args (tptp.y)) % 0.36/0.55 (step @p23 :rule cong :premises (@p22) :args (@t20)) % 0.36/0.55 (step @p24 :rule trans :premises (@p23 @p21)) % 0.36/0.55 (step @p25 :rule nary_cong :premises (@p24 @p20) :args (@t21)) % 0.36/0.55 (step @p26 :rule trans :premises (@p25 @p19)) % 0.36/0.55 (step @p27 :rule quant-var-elim-eq :args ((= (forall @t25 (or (not (= @t22 tptp.y)) @t24 @t23)) @t21))) % 0.36/0.55 (step @p28 :rule refl :args (@t23)) % 0.36/0.55 (step @p29 :rule refl :args (@t24)) % 0.36/0.55 (step @p30 :rule eq-symm :args (tptp.y @t22)) % 0.36/0.55 (step @p31 :rule cong :premises (@p30) :args (@t24)) % 0.36/0.55 (step @p32 :rule nary_cong :premises (@p31 @p29 @p28) :args (@t26)) % 0.36/0.55 (step @p33 :rule aci_norm :args ((= @t27 @t26))) % 0.36/0.55 (step @p34 :rule trans :premises (@p33 @p32)) % 0.36/0.55 (step @p35 :rule cong :premises (@p34) :args (@t28)) % 0.36/0.55 (step @p36 :rule trans :premises (@p35 @p27)) % 0.36/0.55 (step @p37 :rule trans :premises (@p36 @p26)) % 0.36/0.55 (step @p38 :rule aci_norm :args ((= (or false @t16) @t16))) % 0.36/0.55 (step @p39 :rule refl :args (@t16)) % 0.36/0.55 (step @p40 :rule eq-refl :args (tptp.x)) % 0.36/0.55 (step @p41 :rule cong :premises (@p40) :args (@t29)) % 0.36/0.55 (step @p42 :rule trans :premises (@p41 @p21)) % 0.36/0.55 (step @p43 :rule nary_cong :premises (@p42 @p39) :args (@t30)) % 0.36/0.55 (step @p44 :rule trans :premises (@p43 @p38)) % 0.36/0.55 (step @p45 :rule quant-var-elim-eq :args ((= (forall @t34 (or (not (= @t31 tptp.x)) @t33 @t32)) @t30))) % 0.36/0.55 (step @p46 :rule refl :args (@t32)) % 0.36/0.55 (step @p47 :rule refl :args (@t33)) % 0.36/0.55 (step @p48 :rule eq-symm :args (tptp.x @t31)) % 0.36/0.55 (step @p49 :rule cong :premises (@p48) :args (@t33)) % 0.36/0.55 (step @p50 :rule nary_cong :premises (@p49 @p47 @p46) :args (@t35)) % 0.36/0.55 (step @p51 :rule aci_norm :args ((= @t36 @t35))) % 0.36/0.55 (step @p52 :rule trans :premises (@p51 @p50)) % 0.36/0.55 (step @p53 :rule cong :premises (@p52) :args (@t37)) % 0.36/0.55 (step @p54 :rule trans :premises (@p53 @p45)) % 0.36/0.55 (step @p55 :rule trans :premises (@p54 @p44)) % 0.36/0.55 (step @p56 :rule nary_cong :premises (@p55 @p37) :args ((and @t37 @t28))) % 0.36/0.55 (step @p57 :rule alpha_equiv :args (@t43 @t44 (@list @t22))) % 0.36/0.55 (step @p58 :rule alpha_equiv :args (@t48 @t44 (@list @t31))) % 0.36/0.55 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t49)) % 0.36/0.55 (step @p60 :rule quant-miniscope-and :args ((= (forall @t6 (and @t47 @t42)) @t49))) % 0.36/0.55 (step @p61 :rule trans :premises (@p60 @p59)) % 0.36/0.55 (step @p62 :rule trans :premises (@p61 @p56)) % 0.36/0.55 (step @p63 :rule bool-or-and-distrib :args (@t46 @t41 true @t39 false)) % 0.36/0.55 (step @p64 :rule cong :premises (@p63) :args ((forall @t6 (or @t50 @t39)))) % 0.36/0.55 (step @p65 :rule trans :premises (@p64 @p62)) % 0.36/0.55 (step @p66 :rule refl :args (@t38)) % 0.36/0.55 (step @p67 :rule refl :args (@t3)) % 0.36/0.55 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t3 @t38))) % 0.36/0.55 (step @p69 :rule symm :premises (@p68)) % 0.36/0.55 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.36/0.55 (step @p71 :rule cong :premises (@p70) :args (@t51)) % 0.36/0.55 (step @p72 :rule refl :args (@t50)) % 0.36/0.55 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t52)) % 0.36/0.55 (step @p74 :rule cong :premises (@p73) :args ((forall @t6 @t52))) % 0.36/0.55 (step @p75 :rule trans :premises (@p74 @p65)) % 0.36/0.55 (step @p76 :rule refl :args (@t51)) % 0.36/0.55 (step @p77 :rule bool-or-de-morgan :args (@t45 @t40 false)) % 0.36/0.55 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or (not @t53) @t51))) % 0.36/0.55 (step @p79 :rule bool-and-de-morgan :args (@t53 @t3 true)) % 0.36/0.55 (step @p80 :rule trans :premises (@p79 @p78)) % 0.36/0.55 (step @p81 :rule cong :premises (@p80) :args (@t55)) % 0.36/0.55 (step @p82 :rule trans :premises (@p81 @p75)) % 0.36/0.55 (step @p83 :rule cong :premises (@p82) :args (@t56)) % 0.36/0.55 (step @p84 :rule exists-elim :args ((= (exists @t6 @t54) @t56))) % 0.36/0.55 (step @p85 :rule trans :premises (@p84 @p83)) % 0.36/0.55 (step @p86 :rule refl :args (@t3)) % 0.36/0.55 (step @p87 :rule eq-symm :args (@t2 tptp.y)) % 0.36/0.55 (step @p88 :rule eq-symm :args (@t2 tptp.x)) % 0.36/0.55 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t4)) % 0.36/0.55 (step @p90 :rule nary_cong :premises (@p89 @p86) :args (@t5)) % 0.36/0.55 (step @p91 :rule cong :premises (@p90) :args (@t7)) % 0.36/0.55 (step @p92 :rule trans :premises (@p91 @p85)) % 0.36/0.55 (step @p93 :rule cong :premises (@p92) :args (@t9)) % 0.36/0.55 (step @p94 :rule cong :premises (@p12 @p93) :args (@t12)) % 0.36/0.55 (step @p95 :rule cong :premises (@p94) :args (@t13)) % 0.36/0.55 (step @p96 :rule trans :premises (@p95 @p18)) % 0.36/0.55 (step @p97 :rule eq_resolve :premises (@p1 @p96)) % 0.36/0.55 (step @p98 :rule eq-symm :args (@t63 @t64)) % 0.36/0.55 (step @p99 :rule refl :args (@t58)) % 0.36/0.55 (step @p100 :rule refl :args (@t65)) % 0.36/0.55 (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t65 @t58))) % 0.36/0.56 (step @p102 :rule symm :premises (@p101)) % 0.36/0.56 (step @p103 :rule eq_resolve :premises (@p100 @p102)) % 0.36/0.56 (step @p104 :rule refl :args (@t60)) % 0.36/0.56 (step @p105 :rule refl :args (@t66)) % 0.36/0.56 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t66 @t60))) % 0.36/0.56 (step @p107 :rule symm :premises (@p106)) % 0.36/0.56 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.36/0.56 (step @p109 :rule nary_cong :premises (@p108 @p103) :args (@t67)) % 0.36/0.56 (step @p110 :rule eq-refl :args (@t67)) % 0.36/0.56 (step @p111 :rule refl :args (@t67)) % 0.36/0.56 (step @p112 :rule beta-reduce :args (@t68)) % 0.36/0.56 (step @p113 :rule cong :premises (@p112 @p111) :args (@t68)) % 0.36/0.56 (step @p114 :rule trans :premises (@p113 @p110)) % 0.36/0.56 (step @p115 :rule refl :args (@t57)) % 0.36/0.56 (step @p116 :rule ho_cong :premises (@p11 @p115)) % 0.36/0.56 (step @p117 :rule cong :premises (@p116 @p111) :args ((= @t69 @t67))) % 0.36/0.56 (step @p118 :rule trans :premises (@p117 @p114)) % 0.36/0.56 (step @p119 :rule true_elim :premises (@p118)) % 0.36/0.56 (step @p120 :rule trans :premises (@p119 @p109)) % 0.36/0.56 (step @p121 :rule eq-refl :args (@t63)) % 0.36/0.56 (step @p122 :rule refl :args (@t63)) % 0.36/0.56 (step @p123 :rule beta-reduce :args (@t70)) % 0.36/0.56 (step @p124 :rule cong :premises (@p123 @p122) :args (@t70)) % 0.36/0.56 (step @p125 :rule trans :premises (@p124 @p121)) % 0.36/0.56 (step @p126 :rule ho_cong :premises (@p5 @p115)) % 0.36/0.56 (step @p127 :rule cong :premises (@p126 @p122) :args ((= @t71 @t63))) % 0.36/0.56 (step @p128 :rule trans :premises (@p127 @p125)) % 0.36/0.56 (step @p129 :rule true_elim :premises (@p128)) % 0.36/0.56 (step @p130 :rule cong :premises (@p129 @p120) :args (@t72)) % 0.36/0.56 (step @p131 :rule trans :premises (@p130 @p98)) % 0.36/0.56 (step @p132 :rule cong :premises (@p131) :args (@t73)) % 0.36/0.56 (step @p133 :rule refl :args (@t74)) % 0.36/0.56 (step @p134 :rule nary_cong :premises (@p133 @p132) :args (@t75)) % 0.36/0.56 ; WARNING: add trust step for TRUST % 0.36/0.56 ; trust TRUST THEORY_LEMMA % 0.36/0.56 (step @p135 :rule trust :premises () :args (@t75)) % 0.36/0.56 (step @p136 :rule eq_resolve :premises (@p135 @p134)) % 0.36/0.56 (step @p137 :rule chain_m_resolution :premises (@p136 @p97) :args ((not @t76) (@list true) (@list @t74))) % 0.36/0.56 (step @p138 :rule cnf_or_neg :args (@t64 0)) % 0.36/0.56 (step @p139 :rule cnf_and_pos :args (@t62 0)) % 0.36/0.56 (step @p140 :rule reordering :premises (@p139) :args ((or @t61 @t63))) % 0.36/0.56 (step @p141 :rule bool-double-not-elim :args (@t62)) % 0.36/0.56 (step @p142 :rule refl :args (@t77)) % 0.36/0.56 (step @p143 :rule refl :args (@t76)) % 0.36/0.56 (step @p144 :rule nary_cong :premises (@p143 @p142 @p141) :args ((or @t76 @t77 (not @t63)))) % 0.36/0.56 (step @p145 :rule cnf_equiv_neg2 :args (@t76)) % 0.36/0.56 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 0.36/0.56 (step @p147 :rule reordering :premises (@p146) :args ((or @t62 @t76 @t77))) % 0.36/0.56 (step @p148 :rule chain_m_resolution :premises (@p147 @p137 @p140 @p138) :args (@t61 @t78 @t79)) % 0.36/0.56 (step @p149 :rule cnf_or_neg :args (@t64 1)) % 0.36/0.56 (step @p150 :rule cnf_and_pos :args (@t62 1)) % 0.36/0.56 (step @p151 :rule reordering :premises (@p150) :args ((or @t59 @t63))) % 0.36/0.56 (step @p152 :rule chain_m_resolution :premises (@p147 @p137 @p151 @p149) :args (@t59 @t78 @t79)) % 0.36/0.56 (step @p153 :rule cnf_or_pos :args (@t64)) % 0.36/0.56 (step @p154 :rule reordering :premises (@p153) :args ((or @t58 @t60 @t77))) % 0.36/0.56 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p148) :args (@t77 @t80 @t81)) % 0.36/0.56 (step @p156 :rule bool-double-not-elim :args (@t58)) % 0.36/0.56 (step @p157 :rule bool-double-not-elim :args (@t60)) % 0.36/0.56 (step @p158 :rule refl :args (@t62)) % 0.36/0.56 (step @p159 :rule nary_cong :premises (@p158 @p157 @p156) :args ((or @t62 (not @t61) (not @t59)))) % 0.36/0.56 (step @p160 :rule cnf_and_neg :args (@t62)) % 0.36/0.56 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.36/0.56 (step @p162 :rule reordering :premises (@p161) :args ((or @t58 @t60 @t62))) % 0.36/0.56 (step @p163 :rule chain_m_resolution :premises (@p162 @p152 @p148) :args (@t62 @t80 @t81)) % 0.36/0.56 (step @p164 :rule cnf_equiv_neg1 :args (@t76)) % 0.36/0.56 (step @p165 :rule reordering :premises (@p164) :args ((or @t64 @t63 @t76))) % 0.36/0.56 (step @p166 false :rule chain_m_resolution :premises (@p165 @p163 @p155 @p137) :args (false (@list false true true) (@list @t62 @t64 @t76))) % 0.36/0.56 ) % 0.36/0.56 % SZS output end Proof % 0.36/0.56 % cvc5 exiting %------------------------------------------------------------------------------